Skip to main content

2025 AMC 12B Problem 2

Problem 2 of 25EasierAlgebraNumber Theory

Jerry wrote down the ones digit of each of the first 20252025 positive squares: 1,1, 4,4, 9,9, 6,6, 5,5, 6,6, ….\ldots. What is the sum of all the numbers Jerry wrote down?

Answer choices

Show solution

Solution

The ones digits of 12,22,…,1021^2, 2^2, \ldots, 10^2 are 1,4,9,6,5,6,9,4,1,0,1, 4, 9, 6, 5, 6, 9, 4, 1, 0, which sum to 45.45. The 20252025 terms contain 202202 full blocks (20202020 terms) plus 55 more with digits 1,4,9,6,51, 4, 9, 6, 5 summing to 25.25. The total is 202⋅45+25=9090+25202 \cdot 45 + 25 = 9090 + 25 =9115.= 9115. Thus, the correct answer is D.

More practice

Concepts: units digit · pattern recognition · summation

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.